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The disorder systems host three types of fundamental quantum states, known asthe extended, localized, and critical states, of which the critical statesremain being much less explored. Here we propose a class of exactly solvablemodels which host a novel type of exact mobility edges (MEs) separatinglocalized states from robust critical states, and propose experimentalrealization. Here the robustness refers to the stability against bothsingle-particle perturbation and interactions in the few-body regime. Theexactly solvable one-dimensional models are featured by quasiperiodic mosaictype of both hopping terms and on-site potentials. The analytic results enableus to unambiguously obtain the critical states which otherwise require arduousnumerical verification including the careful finite size scalings. The criticalstates and new MEs are shown to be robust, illustrating a generic mechanismunveiled here that the critical states are protected by zeros of quasiperiodichopping terms in the thermodynamic limit. Further, we propose a novelexperimental scheme to realize the exactly solvable model and the new MEs in anincommensurate Rydberg Raman superarray. This work may pave a way to preciselyexplore the critical states and new ME physics with experimental feasibility.

Exact new mobility edges between critical and localized states